Abstract
It is known that some of the mechanical and/or electrical dynamics can be written in the form called ‘Matrix 2nd-order system’ or ‘2nd-order system’ in short. On the other hand, pole-assignment is a commonly accepted technique in designing a performance guaranteeing regulator for the ordinal state space first order system. Recently, control design problems combining these two, that is, synthesis of a state feedback controller for the 2nd-order systems achieving closed loop pole-assignment while preserving its special form of dynamics, have been investigated. The proposed regulator is ‘numerically robust, ’ in the sense that a little perturbation on system matrices would not cause a large shift on the closed loop poles. But this does not suffice as a solution of the robust controller design problem such that matrices contained in the 2nd-order systems are the interval matrices with their lower and upper bounds given. In this paper, robust pole-assignment of the 2nd-order system with interval matrix uncertainties to a circular region in the LHP is discussed. Based on an evaluation of the perturbation in the coefficient space, we have applied the D-stable set expression in the coefficient space that we have obtained recently to determine the feedback gains. It will be shown that the design will finally be reduced to the problem of finding a solution of at most 16 simultaneous inequalities. Also, a numerical example will be given to illustrate the routine of the proposed design procedure.
